In general, this invention relates to the field of interferometry and, in particular, to the high accuracy measurement of aspherical surfaces and wavefronts in an absolute manner.
Aspherical surfaces have become more and more important in modern optical systems because they offer a higher number of parameters for simplifying systems while optimizing their performance. This can lead to systems with less surfaces, less weight, smaller dimensions and higher states of correction, to mention only a few advantages. This is especially true in fields where a high number of optical surfaces are not practical, like in astronomical telescopes or normal incidence reflecting surfaces for the EUV wavelength of 13.6 nm used for lithography tools where it is mandatory to keep the number of surfaces as low as possible. In such cases, there is no choice but to use aspherical surfaces. With demands for high quality performance for complete systems operating in the EUV-regime, the surface errors of reflecting surfaces within such a system must be kept below 0.1 nm, and the measuring accuracy and precision for such errors must be even higher to be able to produce the surfaces in a deterministic manner. In addition, lens surfaces in multielement lithography lenses operating at wavelengths of 193 nm and 157 nm are made aspherical to lower the number of elements made, which are of rare and expensive materials. In these cases, the departures from a best fitting sphere can be as large as 1000 xcexcm, and the dimensions of such lens surfaces have increased to nearly 500 mm.
In an optical system, the function of any its lens elements is to modify the wavefront transmitted by the individual lens elements according to the optical design of the whole system. If a spherical wave or a plane wave enters such a lens, an aspherical wavefront with a very high departure from the best fitting sphere is produced, depending on the conjugates used in the particular test-configuration. So, even the fundamental single lens element, with either spherical or aspherical surfaces can only be tested properly if one is able to deal with aspherical wavefronts in a test set-up. Moreover, this ability is very important for testing wavefronts transmitted through lens elements because inhomogeneity of the lens material itself can deteriorate the wavefront, even when the surfaces are otherwise free of error.
The measurement of aspherical surfaces and wavefronts has been very difficult because of the large departure from the best fitting sphere. With interferometric measurements, high precision is possible by making the dynamic range of the measurement very small, and for this purpose, the wavefront of the reference wavefront, against which the aspherical wavefront is compared, has to be made aspherically as well to ideally fit the wavefront to be measured completely. In prior art, this has been done either by refractive systems, so called xe2x80x9cnull-lensesxe2x80x9d, or with diffractive elements, so called xe2x80x9ccomputer generated hologramsxe2x80x9d, which alter a wave of known and measurable shape (spherical or preferably plane wave) as it transits the compensation element to fit the design aspherical surface at the location where it is placed in the test-set up by design.
In all these cases, the compensation element must be tested to be sure that the correct wavefront is delivered for comparison. But, it is obvious that the same difficulties exist for this type of testing because, again, an aspherical wavefront is produced. Therefore, only indirect test methods are applied by, for instance, measuring the surface of each lens element used in a null system, which is exclusively built with the help of spherical surfaces. Also, the refractive index of the lens material, the lens thickness and the air-spacing of the lenses are measured carefully. Nevertheless, the final accuracy is questionable because of accumulation of measurement errors and the uncertainty of the homogeneity within the lens material.
There are many methods and apparatus in the prior art for measuring aspherical optical surfaces as, for example: 1. Contacting and non-contacting stylus based profilers; 2. Contacting and non-contacting stylus based coordinate measuring machines; 3. Spherical wavefront interferometers; 4. Lateral and radial shearing interferometers; 5. Interferometers with null lenses in the measurement path; 6. Scanning spherical wave interferometers; 7. Scanning white light interferometers; 8. Sub-aperture stitching interferometers; 9. Interferometers using computer generated holograms-CGHs; 10. Point diffraction interferometers-PDIs; 11. Longer wavelength interferometry; and 12. Two wavelength interferometry. While these techniques have utility for many applications, they are limited in their operational capabilities or precision compared with those needed for today""s evolving lithography applications.
Contacting and non-contacting stylus based profilers mechanically scan the aspherical surface under test, and therefore, are slow because they measure only a few data points at a time. Slow techniques are very susceptible to measurement errors due to temperature variations during the measurement. The same limitations apply to contacting and non-contacting stylus based coordinate measuring machines.
Spherical wavefront interferometers usually require the spacing between the element generating the spherical wavefront and the aspherical surface under test to be scanned thereby increasing the measurement time for the entire surface under test thus introducing another parameter which must be measured, usually by another measurement device, and means, commonly known as stitching, for connecting the data from the various zones which fit as the spacing is scanned.
Scanning white light interferometers have many of the same limitations as spherical wavefront interferometers. Lateral and radial shearing interferometers usually measure the slope of the surface under test and thereby introduce measurement errors during the reconstruction of the surface under test via integration of the slopes. This latter type of limitation applies to differential types of profiling techniques as well.
Sub-aperture stitching interferometers introduce serious measurement errors in the stitching process. Interferometers using computer generated holograms are susceptible to errors introduced by the CGH and stray Moirxc3xa9 patterns. They are also difficult to calibrate, i.e., know the calibration of the CGH. Point diffraction interferometers are a class of spherical wavefront interferometers, and therefore, have many of the same limitations, as well as poor lateral spatial resolution.
None of the prior art approaches is entirely satisfactory since each involves a trade-off that places long lead times on the design of the measurement apparatus and method, requires additional fabrication, increases the difficulty of using and calibrating the measurement apparatus, decreases the accuracy and precision, and greatly increases the cost and delivery time of the aspherical optical element.
As a result of certain deficiencies in prior approaches to measuring aspheres, it is a principle object of the present invention to provide a method(s) and apparatus for high accuracy absolute measurement of aspherical surfaces or aspherical wavefronts, either the surface of the final optical part or the wavefront of the final optical lens element in transmission, or by absolutely qualifying the compensation elements for the measurement of aspheres, being either of the refractive, diffractive of reflective type, therefore enabling other, more productive methods for the measurement of the components to be produced in volume.
It is another object of the present invention to provide method(s) and apparatus for measuring aspherical surfaces and wavefronts with large aspherical departures and surface slopes
It is another object of the present invention to provide method(s) and apparatus for measuring aspherical surfaces and wavefronts with large diameters and clear aperture.
It is yet another object of the present invention to provide method(s) and apparatus which can be adapted in an easy manner to different measurement purposes and aspherical surfaces and wavefronts.
It is still another object of the present invention to provide method(s) and apparatus for measuring aspherical surfaces and wavefronts which can be calibrated absolutely.
It is a further object of the present invention to provide method(s) and apparatus which have highly reduced sensitivity to vibrations when measuring aspherical surfaces and wavefronts.
It is another object of the present invention to provide method(s) and apparatus which have reduced sensitivity to temperature changes in the measurement of aspherical surfaces and wavefronts.
It is yet another object of the present invention to provide method(s) and apparatus which have reduced sensitivity to air turbulence of the gas in the interferometer (measurement) cavity in measuring aspherical surfaces and wavefronts.
It is a further object of the present invention to provide method(s) and apparatus that can work with a light source of a coherence length equal only to the aspherical departure.
It is yet a further object of the present invention to provide method(s) and apparatus which can also work with wavelengths for which only point detectors exist (UV and IR-range).
It is still a further object of the present invention to provide method(s) and apparatus which automatically adjust for the spatial location from where the measurement points are sampled.
It is still another object of the present invention to provide method(s) and apparatus which can be adjusted to the spatial resolution required for the measurement.
It is yet a further object of the present invention to provide method(s) and apparatus which have reasonable speed of measurement.
It is still a further object of the present invention to provide method(s) and apparatus which compute both critical coordinates of the aspherical surface, the radial distance h and the axial distance, z, solely from interferometric measurements and not from the geometrical mapping of the detectors onto the surface.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the detailed description is read with reference to the drawings.
In one aspect of the method and apparatus for measuring aspherical surfaces and wavefronts according to the invention, an aspherical surface is illuminated with a wavefront that fits the shape of the surface only in some locations, which are at the center and a radial xe2x80x9czonexe2x80x9d. In those locations, the surface has the same slope as the illuminating wavefront, i.e., the rays strike the aspherical surface at normal incidence and are reflected back by auto-collimation. It is only in those locations where measurement data points are sampled at the instant of normal incidence.
In one variation of the basic principle, the incidence of the rays is not normal to the surface, but the parts of the surface where the actual measurement points are sampled act again as to image the light source with unit magnification, but in a reversed real image.
According to the invention, the optical path difference between the center and the xe2x80x9czonexe2x80x9d is measured by bringing those rays to interfere with each other and measuring the intensity of the interference. The correct and useful rays for that interference are automatically sampled by the use of an aperture, which is located in the image of the light source.
In accordance with the invention, an aspherical test surface is shifted along the optical axis, and as it travels, the same center-part as before is hit by rays, which later enter the aperture, but now the xe2x80x9czonexe2x80x9d shifts radially to a new location in correspondence with the axial position of the test surface. In each of the radial xe2x80x9czonesxe2x80x9d the criterion of normal incidence or, respectively, the imaging criterion of the light source into the aperture is satisfied. Scanning the aspherical surface axially causes the optical path difference between the rays from the center and the radially moving zone to change, and the measured intensity of the interference is modulated. With a sliding windowing technique and an appropriate phase-measurement algorithm, the phase-information is extracted from the measured intensity, and from the phase, the optical path difference is calculated. This is done with an algorithm that allows computation of not only the axial position, z, on the aspherical surface, but also the lateral height, h, of each radial xe2x80x9czonexe2x80x9d, where the rays are sampled. This is achieved by measuring the optical path difference of the two rays: (1) from the light source to the zone and back to the sampling aperture and (2) from the light source to the center and back to the sampling aperture interferometrically, while also measuring the scanning of the aspherical surface with the help of an external distance measuring interferometer (DMI). Consequently, two quantities are measured with interferometric precision with the condition of autocollimation satisfied where the light rays are incident normal to the surface or, equivalently but more generally, that the light source is imaged onto the sampling aperture with magnification=xe2x88x921.
According to another aspect of the invention, the light source and a corresponding sampling aperture are rings with diameters large enough to be able to resolve the image of the test surface onto the detectors azimuthally and with a ring width that is small enough to isolate the coherent light from the small areas on the test surface that are probed.
It is a special feature of the invention that the detectors are not located in a conjugate to the test surface in the radial direction (i.e., an image of the surface) as is the case for the azimuthal direction, but in a conjugate (i.e., an image) of the light source. With this arrangement, the rays from the center and the xe2x80x9czonexe2x80x9d are made to interfere because they are not separated on the detector but made to be on top of each other. The imaging optics behind the sampling aperture is an anamorphic one, but in the sense of radial coordinates, not Cartesian as in the usual case. This special anamorphic imaging is derived by a holographic optical element (similar to like a Fresnel zone plate). For detectors, PIN diodes, or the like, having similar sensitivity and frequency response are preferred.
According to another aspect of the invention, a test-set up is calibrated absolutely by measuring an aspherical surface of known shape in the same way as an unknown aspherical surface would be probed, i.e., by scanning axially. This known surface could be a parabola, for instance, which can be measured absolutely with the help of a known plane mirror and a known spherical mirror using known procedures available to measure those surfaces in an absolute manner. Another possibility is to use a lens with spherical surfaces used in transmission together with a known auto-collimation mirror. The lens can be measured in transmission beforehand in an absolute manner with the use of other conjugates.